What Does Conv2d Output with 56×56 Input, Kernel 3, Stride 2?

Formula Breakdown

The Conv2d output size formula is:

output_size = floor((input_size - kernel_size + 2 * padding) / stride) + 1

Plugging in the values for 56×56 input:

output = floor((56 - 3 + 2*1) / 2) + 1
output = floor((56 - 3 + 2) / 2) + 1
output = floor(55 / 2) + 1
output = floor(27.5) + 1
output = 28

So the spatial dimensions go from 56×56 to 28×28.

PyTorch Code Example

import torch
import torch.nn as nn

# Define the Conv2d layer
conv = nn.Conv2d(in_channels=64, out_channels=128, kernel_size=3, stride=2, padding=1)

# Create input tensor: (batch, channels, height, width)
x = torch.randn(1, 64, 56, 56)
output = conv(x)
print(output.shape)  # torch.Size([1, 128, 28, 28])

# Verify with formula
expected = (56 + 2 * 1 - 3) // 2 + 1
print(f"Expected output size: {expected}x{expected}")  # 28x28

Architecture Context

This is a strided convolution that halves spatial dimensions. Modern architectures like ResNet and ConvNeXt use this instead of max-pooling for downsampling.

Parameter Count

A Conv2d(64, 128, 3) layer has:

parameters = in_channels * out_channels * kernel_size^2 + out_channels (bias)
parameters = 64 * 128 * 3 * 3 + 128
parameters = 73,856

This layer has 73,856 trainable parameters (73728 weights + 128 bias terms).

Practical Tips

• Memory usage: The output feature map for a single image is 128 × 28 × 28 = 100,352 float values (0.38 MB in float32).
• Batch dimension: Multiply memory by batch size. A batch of 32 uses 12.3 MB for this layer's output alone.
• Same padding rule: For any kernel, setting padding = (kernel_size - 1) / 2 with stride=1 preserves spatial dimensions.

Related Questions

• Conv2d 64×64 Kernel 3 Stride 2 → 32×32
• Conv2d 128×128 Kernel 3 Stride 2 → 64×64
• Conv2d 224×224 Kernel 3 Stride 2 → 112×112
• Conv2d 256×256 Kernel 3 Stride 2 → 128×128
• Conv2d 512×512 Kernel 3 Stride 2 → 256×256